# Aptitude Problems on Numbers Test Paper 3

11) The difference between the digits of a two-digit number is 4. What is the digit in the unit's place? To find out the answer, which of the information given in the statements P and Q is/are sufficient?

P: The difference between the number and the number obtained by interchanging the positions of the digits is 36.

Q: The sum of the digits of that number is 12.

1. Only P is sufficient
2. Only Q is sufficient
3. Both P and Q are needed
4. Either P or Q is sufficient.

Explanation:

Let the ten's digit be x and the unit's digit be (x - 4).
P gives: [10x + (x-4)] - [10(x-4) + x] = 36
This does not give the value of x.

∴Unit's place digit cannot be found.

Q gives: x + x - 4 = 12
2x = 12 + 4
2x = 16
X = 8

Hence, unit's digit: X - 4 = 8 - 4 = 4.

So, only Q is sufficient.

12) The sum of the digits of a two-digit number is 14, and the difference between the digits is 2. Which of the following can be that number?

1. 95
2. 68
3. 86
4. 68 or 86

Explanation:

Let x and y be the two digits. Then
As per the question:
x + y = 14 ...... (i)
And, x - y = 2 .... (ii)
On solving the above two equations, we get:
x = 8, y = 6
Hence, 68 or 86 can be the required number.

13) If one-seventh of a number exceeds its eleventh part by 100, what is the number?

1. 770
2. 1100
3. 1825
4. 1925

Explanation:

Let the number be x. Then,
According to the question 11x-7x=7700
4x=7700
x=1925

14) The difference between two numbers is 1550. If the larger number is divided by the smaller one, the quotient is 6, and the remainder is 20. What is the smaller number?

1. 306
2. 308
3. 310
4. 312

Explanation:

Let the numbers be x and x+1550

As we know: = quotient + remainder

Dividend = divisor * quotient + remainder

So, as per question: = 6 + 20

x + 1550 = 6x + 20

5x = 1530

x = 306

Smaller number = 306

Larger number = 1550 + 306 = 1856

15) The sum and difference of two numbers are 25 and 10 respectively. Find the difference of their squares.

1. 190
2. 200
3. 210
4. 220

Explanation:

Let the numbers be x and y.
As per the question: x + y = 25 and x - y = 8
So, x2 - y2 = (x + y) (x - y)
= 25 * 8 = 200

Aptitude Problems on Numbers Test Paper 1
Aptitude Problems on Numbers Test Paper 2
Aptitude Problems on Numbers Test Paper 4
Problems on Numbers Concepts

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